an apartment building has 15 apartments. there 5 more 2-bedroom apartments than 1- bedroom apartments. how many 2- bedroom apartments are there?

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{5}}} \implies \cfrac{-7 -1}{3 -5} \implies \cfrac{ -8 }{ -2 }\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{4}(x-\stackrel{x_1}{5})[/tex]

[tex]y-1=4x-20\implies y=4x-19\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

0.5 feet of snow

Step-by-step explanation:

6 inches is half of a foot because 1 foot = 12 inches.

6 inches / (12 inches / 1 foot) = 0.5 feet of snow

The orders from the person whose depth was closest to the surface to the person whose depth was the farthest from the surface as:

Brenda < Tim  < Carlton < Ali

Ascending order is a method of arranging numbers from smallest value to largest value. The order goes from left to right. Ascending order is also sometimes named as increasing order. For example, a set of natural numbers are in ascending order, such as 1, 2, 3, 4, 5, 6, 7, 8… and so on.

If the information is sorted from highest to lowest, it is said to be in descending order. For example 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 are arranged in descending order. In other words, if the numbers are arranged from the largest to the smallest number, it is said to be in descending order.

We can write, four friends went scuba diving today,

Ali dove = 70 feet,

Tim went down = 50 feet,

Carl dove = 65 feet,

Brenda reach = 48 feet below sea level.

To determine the order from the person whose death was closest to the surface to the person whose death was the farthest from the surface.

Arrange in ascending order of distance from sea level.

Brenda < Tim  < Carlton < Ali

48feet < 50 feet < 65 feet < 70 feet

Therefore,

The order from the person whose depth was closest to the surface to the person whose depth was the farthest from the surface as:

Brenda < Tim  < Carlton < Ali.

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Answer:

1/2

Step-by-step explanation:

Since 13+13= 26 we know that 13 or 1/2 are girls

Answer:

32⅘

(using indices)

32 = 2⁵

= 2⁵ × 1⅘

= 2²⁰

⁵

= 2⁴ = 16

Answer:

The new yearly salary is $16,800

Step-by-step explanation:

Amount of raise.

5% = 0.05

Multiply the original salary times the percentage of the raise.

$16000 * 0.05 = $800

New salary .

$16000 + $800 = $16,800

One-step Solution

$16000+($16000 * 0.05) =$16,800

Answer:

b = 8 , m = - 5

Step-by-step explanation:

For this question we can use simulteanous equations to solve for m and b.

We first come up with 2 equations.

Given the first condition:

23 = -3m + b

b - 3m = 23 (Equation 1)

Now the Second Condition:

-7 = 2m + b

b + 2m = -7 (Equation 2)

Now, we will use Equation 1 - Equation 2 to eliminate b to solve for m.

-3m - (+2m) = 23 - ( - 7)

- 5m = 30

m = 30 ÷ -6 = -5

Now we substitute m into Equation 1 to solve for b.

b - 3(- 5) = 23

b + 15 = 23

b = 23 - 15 = 8

Answer: m=-6    b=5

Step-by-step explanation:

f(x)=mx+b

f(-3)=23     f(2)=7

[tex]\displaystyle\\\left \{ {{23=(m)(-3)+b} \atop {-7=(m)(2)+b}} \right. \ \ \ \ \left \{ {{23=-3m+b\ \ \ \ (1)} \atop {-7=2m+b\ \ \ \ (2)}} \right.[/tex]

Subtract equation (2) from equation (1):

-30=5m

Divide both parts of the equation by 5:

-6=m

Thus, substitute m=-6 in (2):

-7=(-6)(2)+b

-7=-12+b

-7+12=-12+b+12

5=b

Hence,

y=-6x+5

Answer:between 28000 km and 32000 km

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

[tex](-3-i)+(5+6i) \\ \\ =-3-i+5+6i \\ \\ =2+5i[/tex]

Perimeter of computer chip = 14.428 * ( [tex]10^{-7}[/tex] ) meters .

Given : length = 7.18×10⁻⁷ meters

            breadth = 3.4×10⁻⁹ meters    

To find = perimeter of computer chip

Formula for perimeter of a rectangle :      

Perimeter = 2 ( length + breadth )

Calculations :

Perimeter = 2 [ (  7.18×10⁻⁷ ) + ( 3.4×10⁻⁹ ) ]

On simplifying ,

                = 2 [ [tex]10^{-7}[/tex] ( 7.18 + 0.034 )

            = 2 [  [tex]10^{-7}[/tex] ( 7.214 ) ]

              = 14.428 * ( [tex]10^{-7}[/tex] ) meters

Hence , perimeter = 14.428 * ( [tex]10^{-7}[/tex] ) meters .

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The most reasonable conjecture for the number of triangles in the eighth figure in the pattern is that there are 8 triangles in the eighth figure in the pattern

The given figure represents the given parameter

From the figure, we have the following parameters

When represented as a sequence, we have the following terms

4, 6, 8.....

The above sequence represents an arithmetic sequence with the following properties

First term, a = 4

Common difference, d = 2 i.e. 6 - 4

The most reasonable conjecture for the number of triangles in the eighth figure in the pattern is calculated by the following arithmetic sequence formula

Tn = a + (n - 1) * d

So, we have

T8 = 4 + (8 - 1) * 2

Evaluate

T8 = 18

Hence, the most reasonable conjecture for the number of triangles in the eighth figure in the pattern is that there are 8 triangles in the eighth figure in the pattern

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Answer:

9=11

Step-by-step explanation:

Based on the transformaion of point A, the coordinate of the point she would end up is (3, -4)

The complete question is added at the end of this solution

From the question, we have the following point

Starting point = (-3, 5)

The movement is given as

9 units down and 6 units to the right

The above can be represented mathematically as

(x, y) = (x + 6, y - 9)

When the above translation is applied on point A, we have the following equation

A' = (-3 + 6, 5 - 9)

Evaluate the sum and he difference in the above equation

A' = (3, -4)

Hence, the coordinate of the point she would end up is (3, -4)

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Complete question

The coordinates (the x- and y-values) for point A are (−3, 5).

If Samantha moved point A 9 units down and 6 units to the right, at what point would she end up?

Answer:

y = 8/5

Terms:

3y, -2y, y

Leading term:
3y

Step-by-step explanation:

Subtract by 17 from all sides

[tex]3y+17-17=-2y+25-17[/tex]

Simplify

[tex]3y=-2y+8[/tex]

Add term 2y

[tex]3y+2y=-2y+8+2y[/tex]

Simplify further

[tex]3y + 2y = 5y\\= 5y\\5y = 8[/tex]

Divide all sides by 5

[tex]\frac{5y}{5}=\frac{8}{5}[/tex]

Cancel the current leading term, 5y, simplify one last time

[tex]y=\frac{8}{5}[/tex]

Answer:

y =  [tex]\frac{8}{5}[/tex]  or  [tex]1\frac{3}{5}[/tex]  or  [tex]1.6[/tex]  ✅

Step-by-step explanation:

[tex]3y+17=-2y+25[/tex]

                 ⬆️

Move the variable to the left-hand side and change its sign

              ⬇️

[tex]3y+17+2y=25[/tex]

      ⬆️

Move the constant to the right-hand side and change its sign

                      ⬇️

[tex]3y+2y=25-17[/tex]

   ⬆️

Collect like terms

⬇️

[tex]5y=25-17[/tex]

           ⬆️

Subtract the numbers

       ⬇️

[tex]5y=8[/tex]

  ⬆️

Divide both sides of the equation by 5

  ⬇️

[tex]\frac{5y}{5} =\frac{8}{5}[/tex]

  ⬇️

Solution

[tex]y=\frac{8}{5}[/tex]  ✅

Alternative form

[tex]y=1\frac{3}{5} , y=1.6[/tex]  ✅

I hope this was helpful!

Have a blessed day! (✿◠‿◠)

The expressions matched with their correct pairs is

(-8)(-2.2)     →    17.6

(-3.4)(5)      →    -17

(-9.5)(-2)    →     19

(3.8)(-5)     →    -19

From the question, we are to match the tiles to the boxes to form correct pairs

To do this, we will simplify the expressions

Multiplying

-8 × -2.2

= 17.6

Multiplying

-3.4 × 5

= -17

Multiplying

-9.5 × -2

= 19

Multiplying

3.8 × -5

= -19

Hence, the expressions matched with their correct pairs is

(-8)(-2.2)     →    17.6

(-3.4)(5)      →    -17

(-9.5)(-2)    →     19

(3.8)(-5)     →    -19

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Step-by-step explanation:

based on the story told I expected completely different questions.

but for the actually asked question the whole thing about gaining our not gaining weight is competent irrelevant. ignore it.

so, all we need to do is looking at the row totals.

27.4% of the participants took 1 vitamin.

49.5% of the participants took more than 1 vitamin.

so, 49.5% + 27.4% = 76.9% of all participants are taking vitamins in some form.

therefore, the second answer option is correct.

The probability that the selected number is even is 7/15.

The probability that the selected number is a multiple of 4 is 1/5.

The probability that the selected number is a prime number is 2/5.

Based on the information illustrated, the following can be deduced:

Even numbers = 2, 4, 6, 8, 10, 12, 14.

Multiple of 4 = 4, 8 and 12.

Prime numbers = 2, 3, 5, 7, 11, and 13.

Therefore, the probability that the selected number is even will be:

= 7/15.

The probability that the selected number is a multiple of 4 is:

= 3/15 = 1/5.

The probability that the selected number is a prime number is:

= 6 / 15

= 2/5.

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Answer:

y = -x + 5

Step-by-step explanation:

Parallel lines have the same slope, so the slope of the line we need to find is -1. Substituting into point-slope form, we get the equation to be

[tex]y+2=-(x-7)[/tex]

which rearranges into slope-intercept form as follows:

[tex]y+2=-x+7 \\ \\ y=-x+5[/tex]

Answer:

y=-x+5

Step-by-step explanation:

Answer:

Solutions: x=1.

Step-by-step explanation:

Answer: the bus's speed on the level road was 65 milles per hour

Step-by-step explanation:

Let the bus's speed on the level road is x mph

Hence, the bus's speed on the winding road is (x-20) mph

Thus,

3(x)+5(x-20)=420

3x+5x-100=420

8x-100=420

8x-100+100=420+100

8x=520

Divide both parts of the equation by 8:

x=65 mph

The mean of all ninth grader's scores in the city is 80.32

From the question, we are to determine the mean score for all ninth graders in the city

From the given information,

Mariner High school

Mean score is 75 and the frequency is 265

Everett High school

Mean score is 90 and the frequency is 326

Jackson High school

Mean score is 69 and the frequency is 154

Thus,

The mean score for all ninth graders

= (265×75 + 326×90 + 154×69)/ (265 + 326 + 154)

= (19875 + 29340 + 10626)/745

= 59841/745

= 80.32

Hence, the mean is 80.32

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Answer:

13

Step-by-step explanation:

u multiply 4.50 x 3 it makes it 13.5 so they basically need to pay more .

Step-by-step explanation:

I guess the result is needed again in slope-intercept form.

this is in general

y = ax + b

"a" being the slope, "b" being the y-intercept (y value when x = 0).

when a line is parallel to another line, this means they both have the same slope.

so, we can use the same "a" from the original line : -1

to get "b" we use the given point coordinates :

5 = -1×-3 + b = 3 + b

2 = b

so, the full equation is

y = -x + 2

The following are the results:

[container 1] = aₙ = aₙ₋₁  ₊  4.5 ; a₁ = 0

[container 2] = aₙ = ₋4.5 ₊ 4.5n

[container 3] = 68 , 57 , 46 , 35 , 24, ..

[container 4] = aₙ = 79 ₋ 11n

[container 5] = 12 , 19 , 33 , 40

[container 6] = aₙ = aₙ₋₁ ₊ 7; a₁ = 12

Given the sequence is : 0,4.5,9,13.5,18,..

recursive formula = aₙ=a₍ₙ₋₁₎+4.5 where a₁ = 0

Explicit formula = aₙ = a₁ ₊ (n ₋ 1)4.5

= 0 ₊ (n ₋ 1)4.5

aₙ = ₋4.5 ₊ 4.5n

b. given, we have recursive formula: aₙ = aₙ₋₁  ₋ 11 ; a₁ = 68

here we have the common difference as 11, and the initial term is 68.

hence the sequence will be 68 , 57 , 46 , 35 , 24, ..

Explicit formula = a₁ ₊ (n ₋ 1)11

aₙ = 68 ₊ 11n ₋ 11

aₙ = 79 ₋ 11n

c. the explicit formula is given, aₙ = 5 ₊ 7n

here we have the common difference as 7.

so the sequence is 12,19,33,40

and the recursive formula is aₙ = aₙ₋₁ ₊ 7; a₁ = 12

Hence we get the acquired results.

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If 13 cents per yard is the price, and there was $8.63 left on the card, the yards of ribbon  Leila bought is 49 yards of ribbon.

To determine the number of yards of ribbon Leila bought, we need to calculate the difference between the initial balance on the prepaid debit card and the remaining balance after the purchase.

Initial balance: $15.00

Remaining balance: $8.63

The difference between these two amounts represents the amount spent on the ribbon:

$15.00 - $8.63 = $6.37

Now, we can calculate the number of yards of ribbon by dividing the amount spent by the price per yard:

$6.37 / $0.13 = 49

Therefore, Leila bought 49 yards of ribbon.

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15x+180 is the required expression. Let the number be 'x'. For more than we would use addition.

A mathematical expression is the collection of mathematical symbols that results from the valid combination of numbers and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.

2x + 3 is an illustration of a mathematical expression with a variable. Each and every variable needs to have a coefficient, or a value multiplied by the variable. The number 2 is the coefficient of x in the expression 2x + 3, which translates to 2x times plus 3.

Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing.

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Answer: The preimage and final image are the same point

This applies to every point in the xy plane.

======================================================

Explanation:

Let's say we started with the example point of (5,7)

Put the coordinates of the point into the T(x,y) transformation

We'll replace every x with 5 and every y with 7

So,

T(x, y) = (x+3, y-1)

T(5, 7) = (5+3, 7-1)

T(5,7) = (8, 6)

What does this mean? It means that the original preimage point (5,7) moves to (8,6). This is a shift of 3 units right and 1 unit down.

------------------

Now we'll plug the coordinates of that result, the (8,6), into the transformation of S(x, y) = (x-3, y + 1)

Plug in x = 8 and y = 6 to get...

S(x, y) = (x-3, y + 1)

S(8, 6) = (8-3, 6 + 1)

S(8, 6) = (5, 7)

We have gone from (8,6) to (5,7). We're back where we started.

The second transformation of (x-3, y+1) shifts 3 units left and 1 unit up. Notice both of these undo the original "3 units right and 1 unit down" from earlier. So this is why we get back to the starting point. It's not a coincidence.

Therefore, transformation T and transformation S are inverse transformations of one another. They undo each other. It's like taking a step forward (transformation T) and then taking a step back (transformation S)

In terms of algebra, it's like how multiplication and division are inverses of each other.

As you can probably guess, there's nothing particularly special about (5,7). I chose two random numbers. Pick whatever two favorite numbers you want for x and y. Plug them into T(x,y) and then whatever that result is, plug it into S(x,y) to notice you should get back to your original choice of (x,y). I recommend GeoGebra as a useful tool to help with geometric transformations.

The actual volume of the cylinder is 61.73 cm³

Percentage error is the error introduced in a measurement. The formula for the error is given as :

           Error = Percentage error * measured volume

According to the question we have been given that

                        determined volume of cylinder =  58.8 cm³

                         Percentage error  = 4.98%

thus, error = 4.98% * 58.8

                 = 0.0498 * 58.8

                 = ±2.93 cm³

The formula for the actual volume is given as

 Actual volume = measured volume ± error

                          = 58.8 ± 2.93 cm³

As the error is high we will do addition we get

                         = 58.8 + 2.93 cm³

                         = 61.73 cm³

hence the actual volume is 61.73 cm³

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